Integrated Quantitative Systems Pharmacology model of renal anemia, linking nephron loss → REP-cell attrition → blunted HIF-2α/EPO output, the hepcidin–ferroportin–erythroferrone iron-restriction axis (including the loss of renal hepcidin clearance that is unique to CKD), and inflammatory attenuation of EPOR–JAK2–STAT5 signalling, to the full modern pharmacology stack — ESAs, HIF prolyl-hydroxylase inhibitors, oral and IV iron, anti-IL-6 adjuncts and transfusion — and to the endpoints the trials actually measured.

Scale: 219 nodes · 15 clusters · 333 edges in the map · 30 ODE compartments · 15 prebuilt scenarios · 106 references.

Anemia is nearly universal in advanced CKD, and its central lesion is not simple erythropoietin absence. As the kidney scars, the peritubular interstitial fibroblast-like cells that make EPO — REP cells — are lost and transdifferentiate into myofibroblasts under TGF-β/PDGF, so the capacity to make EPO falls. On top of that, the shrinking nephron mass does less tubular reabsorptive work and therefore consumes less oxygen, so cortical tissue pO₂ is paradoxically near-normal and the hypoxic drive that should scream at the remaining REP cells is blunted. The result is the signature laboratory finding of renal anemia: an EPO level that is numerically normal (~10–20 mIU/mL) but grossly inappropriate for a haemoglobin of 9 g/dL, where an intact kidney would produce hundreds. Layered on this are three amplifiers. First, functional iron deficiency: hepcidin is driven up both by IL-6/STAT3 inflammation and by the loss of its own renal clearance, so ferroportin is degraded, the ~11 mg/day of iron recycled from senescent red cells is trapped in macrophages, and duodenal absorption is capped — stores can look full while the marrow starves. Second, shortened red-cell lifespan (~115 days falling to 70–90 in ESKD) from uremic eryptosis plus dialysis-circuit and GI blood loss, which raises the obligate production demand. Third, direct cytokine suppression of BFU-E/CFU-E and of EPOR–JAK2–STAT5 signal transduction, which is what "ESA hyporesponsiveness" actually means at the molecular level. Therapeutically this is a field with a hard-won lesson: pushing haemoglobin toward normal with escalating ESA doses produced no benefit and excess thrombosis in the Normal-Hematocrit, CHOIR, CREATE and TREAT trials, so guidelines now target a deliberately sub-normal 10–11.5 g/dL. The HIF-PHIs (roxadustat, daprodustat, vadadustat) are interesting precisely because they act on all three amplifiers at once — raising EPO only modestly, suppressing hepcidin, and raising transferrin — instead of flooding the marrow with supra-physiological EPO.

1. CKD substrate — primary insult, nephron loss, hyperfiltration, tubulointerstitial fibrosis, peritubular capillary rarefaction, REP cells and their myofibroblast transdifferentiation, the cortical O₂ paradox, uremic milieu, dialysis modality, residual renal function.
2. Oxygen sensing (PHD–VHL–HIF) — O₂/2-OG/Fe(II)/ascorbate co-substrates, succinate–fumarate competition, PHD1/2/3, FIH-1, HIF-1α and HIF-2α, Pro402/Pro564 hydroxylation, pVHL–E3 ligase, proteasome, ARNT, p300/CBP, HRE, the HIF transcriptional program. This cluster is the HIF-PHI drug target.
3. Erythropoietin — EPO gene 3′ HRE enhancer, renal (~90%) vs hepatic (HIF-2α-inducible) synthesis, GATA-2/NF-κB repression, sialylation and half-life, EPOR homodimer, JAK2, STAT5, PI3K/AKT, MAPK/ERK, BCL-xL, GATA-1/KLF1, SOCS3 feedback, receptor-mediated clearance.
4. Erythropoiesis cascade — HSC → CMP/MEP → BFU-E → CFU-E → proerythroblast → basophilic/polychromatic/orthochromatic erythroblast → enucleation → marrow and blood reticulocytes → RBC mass; ineffective erythropoiesis, marrow fibrosis, haem/globin assembly, RBC lifespan, eryptosis, blood loss, splenic clearance.
5. Systemic iron traffic — dietary iron, DCYTB, DMT1, enterocyte labile pool, ferroportin, hephaestin/ceruloplasmin, transferrin/TIBC/TSAT, TfR1, STEAP3, mitochondrial iron, RE macrophage haem recycling (HMOX1), hepatocyte stores, ferritin, functional vs absolute iron deficiency, NTBI, overload.
6. Hepcidin–ferroportin hub — BMP6/BMP2, hemojuvelin, ALK2/ALK3–BMPR2, SMAD1/5/8, SMAD4, HAMP BMP-RE, HFE/TfR2 iron sensing, TMPRSS6, IL-6→STAT3, renal hepcidin clearance, ferroportin ubiquitination, erythroferrone and its BMP trap, macrophage/enterocyte iron sequestration.
7. Inflammation & ESA hyporesponsiveness — uremic toxins, membrane bioincompatibility, gut dysbiosis, access infection, IL-6/TNF-α/IFN-γ/IL-1β, hs-CRP, NF-κB, oxidative stress, EPOR-signal attenuation, progenitor suppression, secondary hyperparathyroidism, B12/folate/carnitine deficits.
8. ESA pharmacology — epoetin, darbepoetin, methoxy-PEG-epoetin beta; SC depot and flip-flop absorption, bioavailability, target-mediated disposition, half-life spread (8 h → 130 h), EPOR occupancy, protocolised escalation, ERFE induction, and the iron-demand surge that unmasks functional ID.
9. HIF-PHI pharmacology — roxadustat/daprodustat/vadadustat/molidustat/ enarodustat; phosphate-binder chelation of absorption, albumin binding, CYP2C8/UGT1A9/OATP1B1, 2-OG-site PHD inhibition, HIF stabilisation, the coordinated program (EPO↑ + DMT1/DCYTB↑ + transferrin↑ + hepcidin↓), hepatic EPO re-activation, near-physiological EPO peaks, LDL-C lowering, off-target VEGF/glycolysis/EMT.
10. Iron repletion therapy — oral ferrous salts, ferric citrate, sucrosomial/ferric maltol; IV ferric carboxymaltose, iron sucrose, ferumoxytol, ferric derisomaltose, dialysate ferric pyrophosphate citrate; the hepcidin-gated oral absorption ceiling, GI intolerance, RE colloid processing, and the PIVOTAL proactive high-dose strategy.
11. Emerging / adjunct — anti-hepcidin, ferroportin inhibitors, anti-BMP6, anti-IL-6(R), IV ascorbate, transfusion (and its alloimmunisation and iron cost), nutrient repletion, calcimimetics.
12. Haemoglobin, O₂ delivery & cardiac adaptation — Hb, Hct/MCV/MCH, plasma volume dilution, O₂-carrying capacity, compensatory cardiac output, LVH, diastolic dysfunction, myocardial supply–demand mismatch, sympathetic/RAAS activation, the cardio-renal-anaemia triad, Hb cycling.
13. Clinical endpoints — Hb in the KDIGO band, Hb response, transfusion avoidance, FACIT-Fatigue, SF-36/KDQOL, exercise capacity, hospitalisation, MACE/MACE+, eGFR slope/ESKD, mortality, monthly ESA dose and ERI.
14. Safety pathways — Hb overshoot, viscosity, platelet activation, endothelial dysfunction, ESA hypertension, thrombosis (access/VTE/stroke), tumour progression, anti-EPO PRCA; HIF-PHI thrombosis/pulmonary-hypertension/ retinal/cyst-growth concerns; FCM-induced FGF23 → hypophosphatemia, IV iron hypersensitivity, labile-iron oxidative injury and infection risk.
15. Monitoring & titration policy — Hb q2–4 weeks, TSAT/ferritin q1–3 months, reticulocytes/RET-He, hepcidin, soluble TfR/ZPP/%HYPO, hs-CRP, phosphate, blood pressure, the KDIGO ±25% titration algorithm, and the formal hyporesponse workup.

The baseline is self-calibrating. Rather than hard-coding 30 initial conditions, [MAIN] solves the stationary state analytically from the patient descriptors (EGFR0, BASE_HB, FIB, BLUNT, IL6_DRIVE, URE, TSAT0, FERRITIN0, HEPC_BASE, …) and then back-calculates the production constants (KIN_PROG, KIN_HEPC, KIN_IL6, KIN_TIBC, KDEP, LOSS_FE, …) that hold it. Build any virtual patient and the model still starts in balance — verified numerically: every derivative is 0 at t = 0 except EGFR (which is supposed to decline) and THR (a cumulative hazard integral).

Iron balance is closed exactly, on purpose. At steady state reticulocyte delivery equals RBC destruction, so recycling equals erythron utilisation (~11.2 mg/day here); plasma iron therefore balances iff obligate loss equals baseline absorption, and the model sets LOSS_FE = abs0 to enforce that. Consequence: any net iron deficit you observe in a scenario comes from a mechanism the model actually represents — dialysis/GI loss, hepcidin trapping, or a drug-driven demand surge — and never from bookkeeping drift.

• Functional iron deficiency on ESA. ERFE rises, hepcidin falls ~35–45%, and ferritin drains from 147 → 75–106 ng/mL while TSAT stays roughly flat. Stores pay for the new red cells; that store-drain-at-constant-TSAT pattern is the model's central iron-kinetic signature.
• Oral iron futility. Absorption is hepcidin-gated, and hepcidin rises with the very stores oral iron creates, so ferritin climbs to ~429 ng/mL while Hb moves +0.3 g/dL.
• The HIF-PHI fingerprint. EPO peaks only ~3–7× baseline (vs ~45–150× for a Q2W/Q4W ESA bolus), hepcidin drops hardest of any arm, TIBC rises, and LDL-C falls ~8–14%.
• The overshoot penalty. Cumulative thrombotic hazard scales ~4.3× from the maintenance arm to the Hb-normalisation arm, driven by viscosity, MAP and ESA exposure terms.
• Hb cycling. Stopping an ESA lets Hb fall on the RBC-lifespan time constant (weeks, not days) while hepcidin rebounds above baseline as ERFE collapses.

The model was checked two independent ways. First, the entire ODE system was re-implemented from scratch in pure Python with an RK4 integrator and the two implementations were compared — the epoetin-maintenance arm lands on Hb 11.70 g/dL at day 365 in both. Second, the spec was compiled and run under real mrgsolve 1.x (R 4.3.3), which is where the table below comes from. Three defects were found and fixed during this process, and they are worth recording because each was a genuine modelling error rather than a typo:

band = days with Hb in 10–11.5 g/dL · >13 = days above 13 g/dL · Haz = cumulative thrombotic hazard (a ranking index, not an event rate) · EPOmax = peak total erythropoietic signal (mIU/mL equivalent).

How to read this table. The three arms that keep a patient inside the KDIGO band for most of the year are the two HIF-PHI arms (339 and 332 days) and the ESA maintenance dose (170 days). Every arm that pushes harder buys ΔHb and ΔFACIT at the cost of days above 13 g/dL and a rising hazard index — scenario 13 is the model's rendering of the Normal-Hematocrit/CHOIR/TREAT result, and scenario 11 shows the same trade-off arriving through dose escalation in a hyporesponder. Scenario 14 is the only arm with a phosphate signal (nadir 1.49 mg/dL), and setting FCM_FLAG = 0 abolishes it.

With the INIT_FROM_PARAM fix the Shiny app's KDIGO-style titrator (±25% steps every 28 days, hold above the ceiling) behaves the way a clinic does: Hb climbs to 11.77 g/dL by block 6, the dose is stepped down 0.625 → 0.198 au, and Hb settles at 10.40 g/dL — inside the band, with zero days above 13. The open-loop scenarios overshoot precisely because they lack this feedback.

library(mrgsolve); library(dplyr)

# The spec is named *_mrgsolve_model.R, so load it by filename:
mod <- mread_file("ackd_mrgsolve_model.R", project = ".")

# Epoetin alfa 75 U/kg SC three times weekly for a year
tiw <- 7 / 3
out <- mod |>
  param(ESA_WK_UKG = 225) |>
  mrgsim(events = ev(amt = 0.5, cmt = "ESA_SC", ii = tiw,
                     addl = floor(365 / tiw)), end = 365) |>
  as_tibble()

# Switch molecules / classes by parameter, not by editing the model:
#   darbepoetin  : KA_ESA=0.25, F_ESA=0.45, KEL_ESA=0.65
#   roxadustat   : KA_PHI=3.0,  F_PHI=0.85, KEL_PHI=0.55  (dose into PHI_GUT)
#   iron sucrose : FCM_FLAG=0                              (no FGF23 signal)

Dose units: ESA_SC 1.0 au ≈ epoetin alfa 150 U/kg · PHI_GUT 1.0 au ≈ roxadustat 100 mg · FE_GUT/FE_IV in real mg elemental iron · RBC 0.33 ≈ one unit of packed cells.

Then launch the dashboard (8 tabs: patient profile · drug PK · erythropoiesis PD · iron & hepcidin · clinical endpoints · scenario comparison · safety · titration and docs):

shiny::runApp("ackd_shiny_app.R")

• The baseline is pinned. [MAIN] back-calculates KIN_PROG so every virtual patient starts at BASE_HB, including the inflamed one. Raising IL6_DRIVE therefore does not lower the presenting Hb; inflammation shows up as a smaller Hb gain per unit ESA and a tighter iron gate. Always compare hyporesponders at matched dose (scenario 10 vs 3), never by their proportional reserve.
• Drug exposures are in dose-proportional au, first-order, with no target-mediated (EPOR) disposition — so the model cannot speak to concentration-based therapeutic monitoring.
• One lumped HIF activity stands in for HIF-1α and HIF-2α across kidney, liver and gut, so isoform-selective agents are out of scope.
• Hepcidin, ERFE and IL-6 are single well-mixed pools: no hepatic/marrow compartmentalisation, no diurnal rhythm.
• FMAX_ABS = 0.28 comes from iron-deficient healthy volunteers; real CKD patients absorb less, so scenario 9 probably overstates oral-iron store loading.
• The thrombotic hazard ranks arms. It is not calibrated to events/100 patient-years and must not be read as one.
• Long-horizon absolute Hb in the open-loop arms should not be taken literally: no clinician would hold a correction dose for 12 months. Use the titrator for realistic trajectories.

Disclaimer. Educational and research QSP model, built from public literature and trial data. It has not been independently validated or certified, and must not be used for clinical decisions, prescribing, or regulatory submissions. Parameters are illustrative literature-anchored approximations; the references support the structure of each mechanism rather than certifying the numerical value attached to it. Fitting and qualification against real patient data would be required for any applied use.